Preserving shading after cutting a hole
Prior to cutting the new geometry the transitions are smooth because the shading is a function of the average face normals connected to each vertex. Because each of those adjacent face normals is different as you go around the surface of the object, the transition is relatively smooth. It's a cheap but effective trick.

Once you start cutting into a face, you get new geometry which has a number of vertices which are surrounded by faces which have the same face normals, therefore the shading is 'flat' on those sections. The transition from surrounding faces onto that flat area is also abrupt, and more prominent with transitions between quads and triangles.

Read Blender docs about custom normals

possible solutions


A way out of that is to carefully adjust the positions of the new vertices such that they follow the inferred curvature, this doesn't have to be exact. as long as you get away from the faces all having the same normals on that spot.


The dark area just below the blue arrow indicates the flow that your geometry would need to have (seen from the side of that edited face). If you can move the internal vertices to match the curvature you'll get reasonable smoothing. 
or adjust the vertex normals to follow the curvature, but (May 2015) this is not exposed to the UI, but can be scripted. Manual changes  might be overwritten by operations such as remove doubles / recalc normals.


Normal Edit modifier.  It takes a vertex group, and an object, and modifies the normals of the vertices in the vertex group to follow as if they eminated from the center of the object (radial) or directionally if you use a mesh object to help guide the normals.


Blender's Proportional Editing feature can help get nice curvature, but you'll have to experiment with it.